Question #1 - A lake contains 587 fish, 91 of which have been tagged by scientists. A researcher randomly catches 13 fish from the lake. What is the probability that exactly 4 of the fish are tagged?

Question #2 - In New Jersey's Pick 6 lottery game, a bettor selects 6 numbers from 1 to 48 (without repetition), and a winning 6-number combination is later randomly selected. Find the probability of getting exactly 4 winning numbers with one ticket.

Question #3 - A small voting district has 109 Republican voters and 135 Democrat voters. A random sample of 20 voters is drawn. What is the mean number of Republicans in such a sample? =

Question #4 - In New Jersey's Pick 6 lottery game, a bettor selects 6 numbers from 1 to 54 (without repetition), and a winning 6-number combination is later randomly selected. What is the mean number of correct numbers in the 6-number combination? =